In this homework, you will be asked to solve the same LP problem using three different approaches, including the normal simplex method and the revised simplex method. You can then compare how the each iteration work between these two methods. Consider the following LP that is also discussed in the lecture, which we denote as problem (P): (P) max19x1+13x2+12x3+17x4s.t.3x1+2x2+x3+2x44x1+3x2+3x3+4x4225,x1+x2+x3+x4117,420,x1,x2,x3,x4,x5,x6,x70. Problem 1 (20 pts): Solve the problem (P) using the normal simplex method (similar to the last problem in HW2). Follow the next instructions to get full credits: (a) For entering variables, use Dantzig's pivot rule (i.e. the largest coefficient rule). (b) Write down the complete dictionary at each iteration of the simplex method, including the initial dictionary constructed from the original problem. (c) For each dictionary, clearly indicates the next entering variable as well as the leaving variable, or declare the problem (dictionary) is optimal. (d) Finally, write down the optimal solution ((x1,x2,x3,x4)=) and the optimal value for this problem. (Hint: There are a total of four dictionaries, including the initial and the optimal dictionary. The third dictionary is provided in the lecture note for you to compare your answer, but don't forget to write down the basis index B and non-basis index N following the instructions.)